Griesmer bound and constructions of linear codes in b-symbol metric

• Main Authors: Luo, Gaojun, Ezerman, Martianus Frederic, Guneri, Cem, Ling, San, Özbudak, Ferruh
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2024
• Subjects: Mathematical Sciences; b-symbol metric; Cyclic code
• Online Access: https://hdl.handle.net/10356/181878
• Institution: Nanyang Technological University

The b-symbol metric is a generalization of the Hamming metric. Linear codes in the b-symbol metric have been used in the read channel whose outputs consist of b consecutive symbols. The Griesmer bound outperforms the Singleton bound for Fq-linear codes in the Hamming metric, when q is fixed and the length is large enough. This scenario is also applicable in the b-symbol metric. Shi, Zhu, and Helleseth recently made a conjecture on cyclic codes in the b-symbol metric. In this paper, we present the b-symbol Griesmer bound for linear codes by concatenating linear codes and simplex codes. Based on cyclic codes and extended cyclic codes, we propose two families of distance-optimal linear codes with respect to the b-symbol Griesmer bound.